Joydeep Das
HPC & Physics Researcher | Plasma Simulations | Machine Learning
Let's connect on HPC, simulations, and research. Contact me for any queries.
Email - joydeep.das39@gmail.com
In addition to solids, liquids, and gases, plasma-filled particles dominate the state universe, especially in stars. Generally, challenged by particle recombination, plasma stability can be maintained at high temperatures as described by the Saha equation. This stable plasma state is essential for fusion reactions, studied in devices called tokamaks, which limit the plasma to the temperature needed to fuse. Aditya-u Tokamak in India and DIII-D in the USA are notable examples.
Due to the accumulated errors in the Euler method, the grid points deviate from the desired flux surfaces, causing errors in the stability of the magnetic field geometry A robust method is needed to ensure renewal The (R,Z) coordinates remain on the same flow surface, allowing for a more accurate and robust mesh representation. This optimized mesh can then be successfully used in particle dynamics simulations, providing higher resolution than standard equilibrium solvers. Addressing this issue could improve the investigation of particle tracking and confinement in plasma physics.
Equlibrium Magnetic Field and its covariant components are given by:
\[ \vec{B} = \nabla \psi (R,Z) \times \nabla \zeta + \frac{F(\psi)}{R} \mathop \zeta\limits^ \wedge \]
\[{B_R} = - \frac{1}{R}\frac{{\partial \psi }}{{\partial Z}};{B_Z} = - \frac{1}{R}\frac{{\partial \psi }}{{\partial R}};{B_\zeta } = \frac{{F(\psi )}}{R};\]
Employ a higher-order integration method, such as Runge-Kutta, to reduce error accumulation in grid mapping.
Develop or implement an algorithm to iteratively adjust (R, Z) coordinates to remain on the same flux surface, using boundary conditions or constraints based on flux function evaluations.
Use gradient-based techniques (e.g., finite difference methods) to correct for drift in flux values, maintaining the correct flux surface alignment of each grid point.
Create adaptive or denser grids in critical regions, such as near magnetic axis points, where particle dynamics require higher precision.
Apply interpolation methods (e.g., spline, linear) or re-meshing for redistributing grid points across flux surfaces more effectively, maintaining density in areas of high field gradient.
SciPy (Python) or MATLAB for advanced numerical methods, including Runge-Kutta integration and interpolation techniques.
Matplotlib (Python) or ParaView for visualizing grid alignment with flux surfaces and observing any drift in (R, Z) coordinates over time.
OpenMP or MPI to optimize computational load when refining or redistributing dense grids for large-scale simulations.
Implement the solution in plasma simulation codes written in Fortran if working with tools like GTC or other PIC-based particle simulation models to maintain compatibility with existing frameworks.
Use equilibrium solvers like VMEC or EFIT to provide baseline flux surfaces for initial conditions or comparisons when validating grid corrections.
The grids do not coincide with flux function due to error accumulated in Eulers’s ,method. Another condition to check that new (R,Z) coordinate remains at same flux function is needed to resolve that. Finally, this grid can be effectively used to work with particle dynamics, as they are much dense other than what obtained from equilibrium solvers.
Let's connect on HPC, simulations, and research. Contact me for any queries.
Email - joydeep.das39@gmail.com